We're starting from the top of tree, searching node with cat_parent_id = '', and then we descend deeper and search chidren of that found parent (cat_parent_id = '$k'), returning array of found children from top to bottom, so in the end you have nice array that you join or use it other way.

use strict;
use v5.10;

my $hash = {
  '986172' => {
    'cat_parent_id' => '',
    'cat_name' => 'Category1'
  },
  '986178' => {
    'cat_parent_id' => '986177',
    'cat_name' => 'Category4'
  },
  '986177' => {
    'cat_parent_id' => '986176',
    'cat_name' => 'Category3'
  },
  '986176' => {
    'cat_name' => 'Category2',
    'cat_parent_id' => '986172'
  }
};

sub rec {
  my ($hash, $parent) = @_;
  my @str;
  foreach my $k (keys %{ $hash } ) {
    if ($hash->{$k}->{cat_parent_id} eq $parent) {
      push @str, $hash->{$k}->{cat_name};
      push @str, rec($hash, $k);
      last;
    }
  }
  return @str;
}

my @arr = rec($hash, '');

say join(',', @arr);

[download]

UPDATE:

Slightly changed recursive function so it won't check categories that was already $seen as parents. We don't know if we could just delete $hash->{$k} after we found it and extract cat_name, $hash could be needed later, so it's only grep { not exists $seen->{$_}}

sub rec {
  my ($hash, $parent, $seen) = @_;
  my @str;
  foreach my $k (grep { not exists $seen->{$_} } keys %{ $hash } ) {
    if ($hash->{$k}->{cat_parent_id} eq $parent) {
      push @str, $hash->{$k}->{cat_name};
      $seen->{$k} = 1;
      push @str, rec($hash, $k, $seen);
      last;
    }
  }
  return @str;
}

[download]

In reply to Re: Organizing data from a hash by alexander_lunev
in thread Organizing data from a hash by audioboxer

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.